Show that the relation y^2 - x^3 + 8 = 0 implicitly defines a solution to the nonlinear equation dy/dx = 3x^2/2y.

Q: 3. (4x³y5 sin 3x + 3x*y$ cos 3x) dx + 5x*y* sin 3x dy = 0 y(0) = 1

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Q: Show that ¢(x) = Ce³* + 1 is a solution to dy/dx – 3y = -3 for any choice of the constant C. Thus,…

A: We have to check Q(x)=Ce3x+1 is solution of given differential equation.

Q: Find both first partial derivatives. 18y2 x az %3D ax dz ду

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Q: Show that y = -cosx In(secx + tanx) is a solution of y" +y = tanx

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Q: What is the differential equation of the orthogonal trajectories of the family of curves x-3xy- 2y²…

A: This is a simple question based on differential equations which could be solved using the basic…

Q: Find the value of 0z/0x at the point (1, 1, 1) if the equation xy + z3x - 2yz = 0 defines z as a…

A: Given, the equation is xy + z3x – 2yz = 0 and defines z as a function of the two independent…

Q: 2+ yety y' : 2у - хеху

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Q: find particular solution of (16x+5y)dx+(3x+y)dy=0. If the curve to pass thru the point (1,-3)

A: Given: 16x+5ydx=-3x+ydydydx=-16x+5y3x+y               It is a homogenous differential equation.…

Q: Differentiate implicitly to find the first partial derivatives of z                              x2…

A: Given that function, x2 + y2 + z2 = 1 Differentiate with respect to x on both sides,…

Q: . Find P.S. of (16x +5y) dx + (3x+y) dy = 0 of the curre to pass thru the point (1,-3) 2. Find P.S.…

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Q: Write in your words about some of the applications of the partial differential equations

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Q: x3sec2y dy/dx+3x2tan y=cos

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Q: The differential equation of the family of curves orthogonal to x² + y? = C² is

A: Solve the above questions.

Q: 2 Express the flowing equation in Cartesian equationr = 1-cos e

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Q: 2. Find dy/dx by implicit differentiation: 5x^2y+5y^2x=-3

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Q: Find the value of ∂x/∂z at the point (1, -1, -3) if the equation xz + y ln x - x2 + 4 = 0 defines x…

A: Given equation is xz+ylnx-x2+4=0. Given point is 1,-1,-3. Partial derivative of given equation with…

Q: What is the differential equation of the orthogonal trajectories of the family of curves y = Cx ?

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Q: The differential equation ry" + 3y - 7y=seca is normal on any open interval not containing a = 0.…

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Q: find dy/dx

A: y=∫sec x21t2+1dt.

Q: Find both first partial derivatives. z = sinh(7x + 16y) az ax az ду

A: From the given problem: z=sinh7x+16y As we know that: The chain rule: fgx'=f'gx·g'x The Power law:…

Q: S csc“(3y)dy

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Q: y² + y²eG)° + 2x²•G° x': 2xye 6) Zaye*

A: The solution is given as

Q: Find both first partial derivatives. z = 4y²/x az ax az ду || ||

A: z=4y2x

Q: a. the root of the given nonlinear equation on its 16th iteration?

A: Given,         y=x3-x2-x-1;      -1<x<4

Q: In substituting the point (4,1,2) in the partial derivatives, why does the terms without x and y…

A: In part (2), we have the following: ∂g∂x4,1,2=-π1 sin4π -14-1 ln3log332 Now, sin4π=0 So,…

Q: 23, zax + sec(x)cos(y) 0, y(0) = 0

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Q: 6. Show that 2y2 dy x² + y2 dx is homogenous equations. Hence, solve the equation.

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Q: Form the partial differential equation from z ax + by + ab by eliminating the constants

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Q: What are the order and degree of the differential equation representing the family of parabolas y2 =…

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Q: Differentiate implicitly to find the first partial derivatives of z. 7x2 + 5y2 + 2z2 = 25 az ax dz

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Q: 5. The integrating factor of the di equation 2y dx + (x- x^3 y^3) O x*3 y^2 O Does not exist

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Q: 5/(A)Evalute ex² dxdy. (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

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Q: Find all the second order partial derivatives of g(x.y) =xy +5 sin (y) + 4y cos (x). please solve

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Q: Find both first partial derivatives. z = sinh(7x + 5y) az ax az ду || ||

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Q: dy 2. 2xy da 3. 2ydx + x (x² In y – 1)

A: We are asked to solve differential equations.

Q: Classify the partial differential equation +34 = sin(3x + 4y).

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Q: Find all the second partial derivative T = e-4r cos(0) -4r, Trr 16e 'cos (0) %3D Tre = 4e -4r,…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: v = exy In(x +y)

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Q: Evaluate the integrals

A: Given integral is:

Q: Find all the second partial derivatives (including fxy etc.) a) v = sin(2s^2 − t^3)

A: Please see the explanation below

Q: Classify the partial differential equation uxx-2 sinx uxy - cos^2x uxy- cosx uy=0

A: Given Partial differential equation is  uxx-2 sinx uxy - cos^2x uxy- cosx uy=0

Q: ry' = 3y + y? ху

A: Solution of a nonlinear differential equation

Q: Find explict solution of the foilowing initial-value problem dy yoanx?, yla)of %3D dx

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Q: (b) Form the partial equation by eliminating function f from z = f(x?

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Q: using partial differential equ

A: Charpit's auxiliary differential eqs are

Q: Find at x = -2 if y = - 4x² + 3 and dy dt dy dt = dx dt - 1.

A: Topic = Derivative As per guidelines , at a time only one question can be answered. pleas repost for…

Q: Obtain the particular solution. 1. 2y dx = 3x dy ; when x = 2 , y = -1 .

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